ECL
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To calculate an Eclipfe of the Moo...
1. For the given Time of the mean full Moon, compute the Moon's Diftance from the Node ; to find whether there be an Eclipfe or not : As taught in the firft Problem.
2. Compute the Time of the true full Moon, with the Sun and Moon's true Place reduced to the Ecliptic.
3. For the Time of the true full Moon, compute the Moon's true Latitude, the Diftance of each Luminary from the Earth, with the Horizontal Parallaxes, and apparent Semi-diameters.
4. For the fame Time, find the Sun and Moon's true Horary Motion.
5. Find the apparent Semi-diameter of the Shadow. And 6. The Arch between the Centres A I, with the
Arch LI.
-. Compute the Scruples of half Duration IN.
And thence, 8. Determine the Beginning, Middle, and End of the Eclipfe.
Laftly, Find the Scruples Eclipfed, and thence the uantity of the Eclipfe : as taught under the preceding Problems.
E.gr. Anno. 1708, the mean full Moon fell on the 29 th Day of September, at ;!■ 45' 4 Afternoon : And then the Moon's Diftance from the afcending Node, was 5 22' $6. Confcquently the Full Moon was Eclipfed. Now, for that Time, we find
True full Moon True Place of the Sun Moon'sPlace in the Ecliptic Moon's True Latit. North Horizont. Parallax, of o of a Apparent Semi-diam. of o of D True Horar. Mot. of D from O Semi-diam. of Shadow Arch between the Centres Arch LI Scruples of half Duration Scruples Eclipfed Duration of Eclipfe Beginning Middle End Quantity 5 Dig. 13'.
To draw a Type, or Figure of a Lunar Eclipfe 071. a 'Plane.
1. Let CD, (Fig. 58.) reprefent the Ecliptic ; and let the Centre of the Shadow be in A : Thro' which draw a right Line G A, perpendicular to D C : And fupppofe D the Eait, C the Weft, A the South, and G the North.
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the Moon, viewed from the Sun, is left than the Aogre«ate of the apparent Semi-diameter of the Sun and Moon Solar Ecllpfes, therefore, happen when the Moon is in Conjunction with the Sun, in, or near the Nodes 7'. e. at the new Moons. Confequently, the memorable Eclipfe of the Sim, at our Saviour's Pafiion, happening at the Time ol full Moon, when the Sun and Moon are in Oe-pofitlon was preternatural. See Conjunction, Opposition,^.*
Tho' the New Moon cover the Sun from the Earth yet is not there an Eclipfe every new Moon ; by Reafon the Moon's Way is not precifely under the Ecliptic, but placed obliquelv thereto ; only interfering it twice in every Period. So that Ecllpfes can only be occafion'd in fuch new Moons, as happen in thefc Interfefiions or Nodes, or very near them.
In the Nodes, when the Moon has no vifible Latitude, the Occultation is Total: and with feme Continuance, when the Difk of the Moon, in (PerigrfO, appears greater than that of the Sun in Ap>og<eo, and its Shadow is extended beyond the Surface of the Earth ; and, without Conti- nuance, at moderate Diftances, when the Cufp, or Point of the Moon's Shadow, barely touches the Earth. Laftly, out of the Nodes, but near them, the Ecllpfes are partial.
Further, when the Moon, being in' her Apogee, appears much lefs than the Sun ; as happens moft fenfibly, when he is in 'Vengteo : the Cufp of the Lunar Shadow not reach- ing the Earth, Hie becomes in a Central Conjunction with the Sun, yet not able to cover his Difk ; but lets his whole Limb appear like a lucid Ring or Bracelet : hence called an Annular Eclipfe.
The other Circumftances of Solar Eclipfes, are,
1. That none of them are univerfal ; that is, none of them are feen throughout the whole Hemifphere, which the Sun is then above ; the Moon's Difk being much too little, and much too near the Earth, to hide the Sun from the Dili of the Earth, which is fifteen Times bigger than it.
1. Nor dees the Eclipfe appear the fame in all Parts of the Earth, where it is feen; but when in one Place it is Total, in another it is Partial.
3. It does not happen at the fame Time, in all Places where it is feen ; but appears more early to the Weftern Parts, and later to the Eaftern.
4. Its Beginning is always on the Weftern Side the Sun, and on the fame Side it ends.
5. In moft Solar Eclipfes, the Moon's darken'd Difk is cover'd with a faint, dawning Light ; which is commonly attributed to the Reflexion of the Light, from the illumi- nated Part of the Earth.
Laftly, In Total Eclipfes of the Sun, the Moon's Limb
is feen furrounded by a pale Circle of Li"ht ; which the
2. From A, with the Interval of the Aggregate A N, of late Aftronomers take for a manifeft Indication of a Lunar
9°
23'
49
6°
43'
47'
6
43
47
43
- 5
6
5*
18
l«
5
15
22
30
12
41
13
43
14
4
5
3«
30
13
21
l"
- 5
a
8"
3
12
9
15
43
to
28
14
the Semi-diameter of the Shadow A P, and of the Moon PN, defcribe a Circle DGCQ_; and with the Interval of the Semi-diameter of the Shadow A P, draw another Concentric Circle E M F R, which will exhibit the Section of the Shadow in the PaSage of the Moon.
3. Let A L be equal to the Latitude of the Moon at the Beginning of the Eclipfe ; and in L erect a perpendi- cular L N, meeting the greater Circle in N, towards the Weft. Then will the Centre of the Moon, at the Begin- ning of the Eclipfe, be in N.
4. After like Manner, make A S equal to the Latitude of the Moon at the End of the Eclipfe ; and in S, erect. a perpendicular O S, parallel to DC: Then will the Centre of the Moon be in O, at the End of the Eclipfe.
5. Connect the Points G and N by a right Line : O N will be the Arch of the Otbit, which the Centre of the Moon defctibes during the Eclipfe.
6. From O and N, with the Interval of the Moon's Semi-diameter, defcribe Circles PV and TX, which will exhibit the Moon at the Beginning and End of the Eclipfe.
7. Then, from A, letting fall a perpendicular A I to ON; the Centre of the Moon will be in I, in the Middle of the Darknefs.
Wherefore, laftly, from I, with the Interval of the Moon's Semi-diameter, defcribe a Circle H K : This will repre- fent the Moon in its grcateft Obfcurity, and at the fame Time the Quantity of the Eclipfe : The Circle P N T, &c. terminating the Shade. 1
Eclipse of the Sun, is an Occultation of the Sun's Body, occafion'd by a diametrical Interpofition of the Moon be- tween the Sun and the Earth. See Sun.
It is diftinguifhed, like that of the Moon, into Total and Tartial, &c. to which muft be added a third Species
Atmofphere. See Atmosphere.
The Aftronomy of Eclipses of the Sun. _To determine the Bounds of a Solar Eclipfe. If the Moon's Parallax were infenfible, the Bounds of a Solar Eclipfe would be determined after the fame Manner as thofe of a Lunar : But by Reafon here is a fenfible Parallax, we mull: alter our Meafurcs a little, viz.
1. Add the apparent Semi-diameters of the Luminaries both in Apogtfo and Perigceo together.
2. Since the Parallax diininiihes the Northern Latitude ; to the former Sum, add the greater}. Parallax of Latitude polfible : And fince the Parallax augments the Southern Latitude, from the fame Sum, fubftraci the grcateft Parallax of Latitude. Thus, in each Cafe, will you have the true Latitude, beyond which there can be no Eclipfe.
This Latitude given, the Moon's Diftance from the Nodes, beyond which Eclipfes cannot happen, is found, as already directed for Lunar Eclipfes.
As different Authors follow very different Hypothecs, with Regard to the apparent Diameters of the Luminaries, and the greateft Parallax of Latitude ; they differ much in align- ing the Bounds at which Solar Eclipfes happen. 'Ptolomy, makes the utmoft Bound of Eclipfes at ip» 25', Diftance from the Node ; Copernicus, at 19° 12'; Tycho, at 18 25'; Kepler, at 17° i<r' ; Ricciolus, at 18° 49'. Tho' Ttolomy, in other Places, judges iff" 42' Minutes diftance from the Node, ncceffary; Copernicus, 16' 25'; Tycho, 17 s'j Kepler, 15° 55 ' ; and Ricciolus, 15° 58'.
To find the Ttigits Ecliffed.
Add the apparent Semi-diameters of the Luminaries into one Sum : From which fubftraci: the Moon's apparent Latitude, the Remainder is the Scruples, or Parts of the Diameter Eclipfed. Then fay, as the Semi-diameter of the Sun is to the Scruples Eclipfed ; fo are 6 Digits reduced
called Annular.
Eclipfes of the Sun, fome Authors obferve, fhould in lnt0 Scruples, or 350 Scruples, to the Digits Eclipsed. Propriety be called Eclipfes of the Earth. Sec Earth. y find the Seru p Ies of Mf Duration, or the Line
As the Moon is found to have a Parallax of Latitude; of Tiuraerfion.
Eclipfes of the Sun only happen when the Latitude of The Method is the fame as that dcliver'd for Lunar Eclipfes.
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